Annals of Statistics

A Complete Class Theorem for Estimating a Noncentrality Parameter

Mo Suk Chow

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Abstract

In statistical decision theory, an important question is to characterize the admissible rules. In this paper, we establish complete class theorems for estimating the noncentrality parameter of noncentral chi-square and noncentral $F$ distributions under squared error loss. Under a minor assumption, any admissible estimator must be a generalized Bayes rule. Using this result, we prove that the positive part of the UMVUE is inadmissible.

Article information

Source
Ann. Statist., Volume 15, Number 2 (1987), 800-804.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350375

Digital Object Identifier
doi:10.1214/aos/1176350375

Mathematical Reviews number (MathSciNet)
MR888440

Zentralblatt MATH identifier
0627.62008

JSTOR
links.jstor.org

Subjects
Primary: 62C07: Complete class results
Secondary: 62C15: Admissibility

Keywords
Complete class theorem noncentrality parameter generalized Bayes rules

Citation

Chow, Mo Suk. A Complete Class Theorem for Estimating a Noncentrality Parameter. Ann. Statist. 15 (1987), no. 2, 800--804. doi:10.1214/aos/1176350375. https://projecteuclid.org/euclid.aos/1176350375


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